Review of Fractions

• Addition

• Common Denominators

• Reducint Fractions (Factoring)

• Multiplication

• Ratios

Fractions

13

Numerator

Denominator

132

Reduced FormSimple Fraction

73

146

Units Extracted

FractionsHow to Add Fractions

1/6 + 1/3 = ?

1/3 + 2/3 = ?To add fractions, they must have a common denominator. Then add the numerators.

Sometimes fractions do not have common denominators to start with. So the first step in adding them is to find a common denominator.

Fractions

1/6 + 1/3 = ?To find a common denominator, multiply one or both fractions by a form of the number one so that they will have the same denominator.

In this case you can multiply 1/3 by 2/2 to turn it into sixths.

13

x 22 = 2

6

16 + 2

6 =36

Then add the fractions with the new common denominator

36

= 12 Finally, reduce the result.

The number one

Fractions

2 1/6 + 3 1/3 Common denominator to add

2 1/6 + 3 2/6

5 3/6

5 1/2

Reduce

FractionsHow to Reduce a Fraction

Factor the numerator and denominator into prime factors.

Cancel all the common factors.

What remains is the reduced fraction.

1830

18 = 32 x 2

30 = 5 x 3 x 2

18 = 32 x 2

30 = 5 x 3 x 2

35

FractionsFinding the Lowest Common Denominator

(or Least Common Multiple)

Factor each number into prime factors. Then take the highest exponent of ALL factors from each number.

9 = 32 15 = 3 x 5

32 x 5 = 45

Highest exponent

Fractions

Find the Least Common Denominator

Reduce

3/9 + 4/15

9 = 32 15 = 3 x 5

(highest number of all factors)

32 x 5 = 4539 5

5 1545

415

33

1245

x

1545

1245

x

+ 2745

3x3x33x3x5

35

Adding using the Least Common Denominator

Fractions

2 1/6 + 3 1/3 Common denominator to add

2 1/6 x 3 1/3Convert to simple fractional form and multiply numerators and denominators

Multiplication

Fractions

In industry most fractional units have to do with measurements of length or mass and are usually decimal if the metric system is used or fractional units of the Old English System (OES).

Length: if it is metric it will be decimal divisions. if it is OES it may be decimal or fractional divisions.Mass: if it is metric it will be decimal divisions. If it is OES it will be in separate units.

8.57 cm. 3 3/8 inches 3.3 inches 3 21/64 inches

Examples:

Fractions

1/2 = 0.51/4 = 0.251/8 = 0.1251/16 = 0.06251/32 = 0.031251/64 = 0.0156251/128 = 0.0078125

Fractions Decimal

Ratios

• Rates, amount of change, complex relationships are often governed by ratios:

A

B

C

D

The units or dimensions on both sides of the equation must be the same

Ratios

A

B

C

D

You can find any one of the variables if you know the other three

A

=

B

C

D

BCD

CDA B

AC

ABD

=

=

=

Ratios

B

C

D

A

B

C

D

A

A = BCD

B CDA=

Ratios

B

C

D

A

B

C

D

A

C ABD=

D BAC=

Ratios1 gallon of water weighs 8 pounds. How much does 360 gallons weigh?

1 gallon

8 pounds

360 gallons

? pounds

360 gallons x 8 pounds1 gallon

2880 pounds